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2028_HW4_120610 - ISyE 2028C HW#4(past ISyE 2028 Exam#3 You...

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ISyE 2028C HW#4 ( past ISyE 2028 Exam #3 ) You only have to work on Problem #2 for HW#4. [20%] (You do not need to do this problem for your HW#4.) Problem #1: Two types of material ( A and B ) are compared for performance of manufactured products. Twenty specimens are used from each material type. Manufacturing process will choose one of the two types of material randomly. The following summary statistics of performance are obtained from testing the products. y A _bar = 83.55, y B _bar = 79.70, s A = 3.663, s A = 3.097. Answer the following questions with detailed steps of calculations. (a) Use the confidence interval idea to test whether σ 1 2 = σ 2 2 . Choose the α value appropriately such that the table value given in the end of the textbook is usable for your answer. Report the interval, the α value and your statistical decision of whether σ 1 2 = σ 2 2 . [10%] (b) Use an appropriate t-test to check whether µ 1 = µ 2 . Use α = 0.05. [10%] [40%] (This is a tricky problem – it requires to use a random effect to model the data ) Problem #2:
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